1. Field of the Invention
The present invention relates to configuring a medium with a two-state atomic system that stores spectra at electromagnetic frequencies, and, in particular, to the use of a chirped field to erase or invert spectra already stored in the medium.
2. Description of the Related Art
Information processing based on optical analog signal processing promises to provide advantages in speed, size and power over current information processing systems. Many versatile optical coherent transient (OCT) processing devices have been proposed. An OCT device relies on broadband complex spatial-spectral grating formed in the optical properties of a material, such as an inhomogeneously broadened transition (IBT) material, also called a spatial-spectral (S2) material. A spatial-spectral grating has the ability to generate a broadband optical output signal that depends on an optical probe waveform impinging on that grating and the one or more interacting optical signals that formed the grating. The optical properties of the spatial-spectral grating at any electromagnetic frequency are determined by the population of atoms in each electron quantum level state of a two-state atomic system.
In optical analog signal processing, the medium is used to store particular spectral features of interest, such as the result of the interaction of one or more optical beams carrying information. See for example, published International Patent application WO 2003/098384 entitled “Techniques for processing high time-bandwidth signals using a material with inhomogeneously broadened absorption spectrum, Inventors: K. D. Merkel, Z. Cole, K. M. Rupavatharam, W. R. Babbitt, T. Chang and K. H. Wagner, 27 Nov. 2003 (hereinafter Merkel), the entire contents of which are hereby incorporated by reference as if fully set forth herein.
In some circumstances, including those described by Merkel, the medium is an optically absorptive medium when most of the population is in the ground state of the two electron quantum level states. This reduces the signal level of a readout beam transmitted through the medium. However, when the population is evenly divided between the two states, and all coherent superposition states have decayed away, the medium is transparent, e.g., signal levels transmitted are essentially equal to the signal levels impinging. Furthermore, when most of the population is in the excited state, the medium is amplifying, e.g., signal levels transmitted are greater than the signal levels impinging.
Once the medium has been endowed with spectral content in the form of frequency dependent or spatially dependent populations, or both, the same portion of the medium can not be reused immediately without contamination by the previously stored spectral content. It is therefore necessary to return the populations of the two states to a uniform level over a range of frequencies, independent of the previously stored spectral content, before processing independent signals in the medium. The process of making population uniform over a frequency range is called erasure.
One approach used to erase spectral content in a frequency range is to wait for the atoms in the excited state to decay to the ground state, so that essentially the entire population of atoms of interest is in the ground state. A disadvantage of this approach is that decay is typically exponential and requires waiting very long times, compared to desirable processing rates, to effectively return the population to the ground state.
Another approach is to add energy to the system so that the entire population is in the excited state, making a uniform spectrum, and wait for the system to decay to a level desired for processing, such as all in the ground state or equal populations in both states. A disadvantage of this approach is that it takes substantial energy. Another disadvantage is that it takes a long time to decay to a desired population distribution, even to equal populations in both states.
Another approach is to write on top of the previously written spectrum with approximately the opposite spectral content, such that the process cancels the previous spectral grating. A disadvantage of this approach is that the spectral content already stored in the medium must be known well. Another disadvantage is that perfect cancellation is not possible due to non-linearities and population decay. Furthermore, the population decay time must be very long compared to the time to perform the erasure, so that the over-write does not impose a lower strength inversion of the original spectrum.
It is sometimes advantageous to invert the population levels, without removing the spectral content. For example, when the spectral content in an absorbing medium is such that most of the atoms are in the ground state, it is advantageous to invert the population levels so that the readout beam signal level is higher. The process of inverting the population of the two states is called inversion. However, no publication known to applicants has addressed inversion of frequency-dependent populations; publications have only addressed uniform populations.
In one approach to inverting a uniform population over a frequency band, a chirped optical field has been used. The frequency and amplitude of the chirped field are as given for a hyperbolic secant in Table 1, described next.
Other two-state atomic systems have been used. For example, in nuclear magnetic resonance (NMR) applications, the populations of atoms in two quantum spin states are measured. These spin states affect the signals emitted at electromagnetic frequencies outside the optical frequency range.
Inversion of a uniform spin population in a two spin system has been proposed, using a variety of functional forms for time dependence of amplitude and frequency, in a series of papers including U.S. Pat. No. 6,064,207, by E. Kupce, entitled “Adiabatic pulses for wideband inversion and broadband decoupling”, May 16, 2000 (hereinafter Kupce), the entire contents of which are hereby incorporated by reference as if fully set forth herein. Table 1 summarizes the functional forms described in these series of publications.
TABLE 1Amplitude and frequency of electromagnetic field for used for uniformpopulation inversion in NMR.NameAmplitude, A(t) =Frequency, ω(t) =Hyperbolic SecantAmax sech(βt)λ tanh(βt)GaussianAmax e−βtλ erf(βt)LorenzianAmax/(1 + (βt)2)λ (arctan(βt) + βt/(1 +(βt)2))/2CosineAmax cos(βt)λ (βt + sin(βt) cos(βt))/2Cosine SquareAmax cos2(βt)λ (12βt + 8sin(βt) +sin(4βt))/32WURST-nAmax(1 − |sin(βt)|n)Kc tIn Table 1, the angle βt runs from −π/2 to +π/2; Amax is the maximum amplitude of the electromagnetic field (the magnetic field in Kupce); κc is a constant chirp rate equal to a constant frequency change per unit time; and n is a large integer. The constant λ is given by Expression 1λ=Amax2/βQ  (1)where Q is an adiabatic factor greater than one. Thus the frequency range scale λ, the temporal duration scale ε, the amplitude scale Amax are related. Kupce also proposes a stretched pulse in which a central part is a constant-amplitude (Amax) linear sweep with constant chirp rate κc, and the rising and falling edges are adiabatic pulses of the form given in Table 1 for βt<0, and βt>0, respectively.
Based on the foregoing, there is a clear need for techniques to configure a medium to eliminate the influence of prior stored spectral features, such as gratings, that do not suffer all the deficiencies of prior approaches.
Based on the foregoing, there is also a need for techniques to configure a medium to invert prior stored, non-uniform spectral features, such as gratings, that do not suffer all the deficiencies of prior approaches.